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Generative modeling for time series via Schrödinger bridge

Author

Listed:
  • Mohamed Hamdouche

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Pierre Henry-Labordere

    (Qube RT)

  • Huyên Pham

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

Abstract
We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with a toy autoregressive model, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets. Finally, we illustrate the SB approach for generating sequence of images.

Suggested Citation

  • Mohamed Hamdouche & Pierre Henry-Labordere & Huyên Pham, 2023. "Generative modeling for time series via Schrödinger bridge," Working Papers hal-04063041, HAL.
    • Handle: RePEc:hal:wpaper:hal-04063041
    Note: View the original document on HAL open archive server: https://hal.science/hal-04063041v1
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    File URL: https://hal.science/hal-04063041v1/document
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    References listed on IDEAS

    as
    1. Jan Gairing & Peter Imkeller & Radomyra Shevchenko & Ciprian Tudor, 2020. "Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1691-1714, September.
    2. Pierre Henry-Labordere, 2019. "From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models," Working Papers hal-02090807, HAL.
    3. Vedant Choudhary & Sebastian Jaimungal & Maxime Bergeron, 2023. "FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs," Papers 2303.00859, arXiv.org, revised Dec 2023.
    4. Magnus Wiese & Robert Knobloch & Ralf Korn & Peter Kretschmer, 2020. "Quant GANs: deep generation of financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 20(9), pages 1419-1440, September.
    5. Hans Buhler & Blanka Horvath & Terry Lyons & Imanol Perez Arribas & Ben Wood, 2020. "A Data-driven Market Simulator for Small Data Environments," Papers 2006.14498, arXiv.org.
    6. Pierre Henry-Labordere, 2019. "From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models," Papers 1904.04554, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Francesca Biagini & Lukas Gonon & Niklas Walter, 2024. "Universal randomised signatures for generative time series modelling," Papers 2406.10214, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    generative models; time series; Schrödinger bridge; kernel estimation; deep hedging;
    All these keywords.

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